Solve (x+1)^2=1

$$( x + 1 ) ^ { 2 } = 1$$

Solve for x

$$x=0$$

$$x=-2$$

Steps Using Factoring

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$x^{2}+2x+1=1$$

Subtract 1 from both sides.

$$x^{2}+2x+1-1=0$$

Subtract 1 from 1 to get 0.

$$x^{2}+2x=0$$

Factor out x.

$$x\left(x+2\right)=0$$

To find equation solutions, solve x=0 and x+2=0.

$$x=0 x=-2$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$x^{2}+2x+1=1$$

Subtract 1 from both sides.

$$x^{2}+2x+1-1=0$$

Subtract 1 from 1 to get 0.

$$x^{2}+2x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}}}{2}$$

Take the square root of 2^{2}.

$$x=\frac{-2±2}{2}$$

Now solve the equation x=\frac{-2±2}{2} when ± is plus. Add -2 to 2.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-2±2}{2} when ± is minus. Subtract 2 from -2.

$$x=-\frac{4}{2}$$

Divide -4 by 2.

$$x=-2$$

The equation is now solved.

$$x=0 x=-2$$

Steps for Completing the Square

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{1}$$

Simplify.

$$x+1=1 x+1=-1$$

Subtract 1 from both sides of the equation.

$$x=0 x=-2$$